Traveling without a Visa

I am currently traveling in Italy and entered the country on Feb. 14. I know I can stay in Italy through May 14 as a tourist without a visa. I would like to go to the UK on May 13 and stay through May 21 and then fly back to the United States for good. I am a US citizen. Do I need to leave Italy for a period prior to May 14 and THEN go to the UK? Please, any advice would be great!